In the present work, we will use a semi-Lagrangian discontinuous Galerkin scheme (sldg). This method, see e.g. [1]}, [2]}, is conservative by construction [3]}, has similar or better properties with respect to limiting diffusion compared to spline interpolation (see [4]} for a comparison), and is completely local (at most two neighboring cells are accessed to update a cell). Thus, it provides a method that in addition to being ideally suited for today's massively parallel CPU and GPU systems, is competitive from a numerical point of view. In addition, a well-developed convergence analysis is available for the Vlasov–Poisson equation
[5]}, [6]}.
